Background: Many problems of combinatorial optimization, which are solvable only in exponential time, are known to be Non-Deterministic Polynomial hard (NP-hard). With the advent of parallel machines, new opportunities have been emerged to develop the effective solutions for NP-hard problems. However, solving these problems in polynomial time needs massive parallel machines and is not applicable up to now. Objectives: DNA (Deoxyribonucleic acid) computing provides a fantastic method to solve NP-hard problems in polynomial time. Accordingly, one of the famous NP-hard problems is assignment problem, which is designed to find the best assignment of n jobs to n persons in a way that it could maximize the profit or minimize the cost. Material and Methods: Applying bio molecular operations of Adelman Lipton model, a novel parallel DNA algorithm have been proposed for solving the assignment problem. Results: The proposed algorithm can solve the problem in O(n2) time complexity, and just O(n) initial DNA strand in comparison with initial sequence, which is used by the other methods. Conclusions: In this article, using DNA computing, we proposed a parallel DNA algorithm to solve the assignment problem in linear time.

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